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-----Message d'origine-----
De : Vladimir Batagelj [mailto:[log in to unmask]] 
Envoyé : mardi 12 janvier 2016 14:18
Objet : Re: How to measure the distribution of an attribute among the nodes of a network?

On 12-01-2016 13:27, LEVALLOIS Clément wrote:
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> Hi,
> Indeed my formulation was not clear. Refining my statement, I think a 
> possible solution can appear:
> - Being evenly distributed in the network would mean that the distance 
> (shortest paths) between the nodes bearing this attribute value is 
> comparably close to the distance between the same number of nodes 
> randomly picked from the entire set of nodes of the network.
> Does it make sense? 2 things:
> - it does not depend on a notion of communities
> - I might be wrong but the formulation above seems quite 
> computationally intensive
> Clement

   If  U is a small community then usually  N(U)  will have large
   intersection with  U  and  N(U) setminus U  will be relatively
   small - the value of  W  will be small.
   We get large values of  W  when  U  is large or  U  contains hubs -
   nodes with very large degree.

   It is very fast. The time complexity is linear in number of links.


Vladimir Batagelj
  IMFM - Institute of Mathematics, Physics and Mechanics
  Jadranska 19, 1000 Ljubljana, Slovenia and
  University of Primorska, Andrej Marušič Institute, Koper
T: +386 1 4766 672
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